Category: Mathematics

When dealing with those pushing pseudoscience, like the antivaccination cult, the most frustrating thing is that they tend to ignore and deny the most basic tenets of science. If denying the fact of gravity would further their goals of “proving” vaccines are neither effective nor safe, they would do so. And now that it’s flu season, they’re producing zombie tropes about flu vaccine ingredients.

If the antivaccination movement didn’t lead to epidemics of long-gone diseases, which can harm and kill children, the conversation would be over. I would just put the vaccine deniers in the same group as evolution deniers (creationists) or gravity deniers (there has to be some, somewhere). I would mock their pseudoscience, and move on. Of course, their denialism does lead to deaths of children, so we have to do what is right, and stop their lies, misinformation and ignorance in every forum we can.

We have to appeal to scientific values, and despite the fact that antivaccination pushers don’t share those values, we must continue to try. I have gotten enough emails and comments from people that they have started to vaccinate because of what I have written, so maybe some child’s life is better because all of us who support vaccines are heard.

Science deniers are an awfully frustrating lot. Statistical evidence seems so cut and dried to me. Unfortunately, the anti-science crowd prefers anecdotes to data. And the abuse of vaccine statistics are the worse.

If science is evidence, then the basis of evidence is statistical reliability. I don’t want to oversimplify statistics, but this branch of mathematics identifies random events. Once again, statistics is difficult to grasp, yet every single paper I’ve ever read (except for the very worst) has fairly easy-to-understand statistics, once you know the lingo.

For example, most papers with vaccine statistics use a term called “relative risk,” or RR. Relative risk is the ratio of the probability of an event occurring in one group (say vaccinated) compared to a control group (not vaccinated).

An RR less than 1.0 implies that the the vaccinated group has a lower risk of an event than the control group. An RR=1.0 means that the risk is the same in both groups. Of course, an RR greater than 1.0 indicates that the vaccinated group has a higher risk than the control group.

And the size of the risk changes as numbers grow much larger or smaller than 1.0.

That statistical measurement seems easy. Undoubtedly, the calculations to reach the RR value are complex, but the top line number is fairly easy to grasp.

Nevertheless, vaccine statistics, despite being fairly straightforward, are often misinterpreted and ignored. Maybe there’s a reason for it? Let’s look.

If you spend any amount of time on the internet researching science and pseudoscience, you’ll find alarming claims about toxic or poisonous substances in our foods, vaccines, air, water, and so much else. And then you’ll find a lot of people (myself included) who try to present science-based evidence that these substances are neither toxic nor poisonous.

Paracelsus, a 16th century Swiss German physician, alchemist, astrologer, is traditionally thought to have founded the discipline of toxicology, an important branch of medicine, physiology, and pharmacology. Paracelsus wrote one of the most important principles of toxicology:

All things are poisons, for there is nothing without poisonous qualities. It is only the dose which makes a thing poison.

In other words, if you’re speaking about substances in foods or vaccines or anything, the most important principle is that the dose makes the poison (or toxin). Everything that we can consume or breathe is potentially toxic, but what is the most overriding principle must be the dose. Continue reading “Simple math – the dose makes the poison”

And once again, this is simple, third grade math. Let’s see if the typical antivaccination cult member can understand this!

The AV nuts are always asking, “If vaccines work so well, why are you concerned about my unvaccinated kid? Aren’t yours protected?” For this discussion, let’s leave out the usual list of people who cannot be vaccinated, the list of people the AV’ers will callously consider not their problem. Let’s not get into the idea that maybe it’s OK for me to worry about their kids too, kids who through no fault of their own are the poker chips these parents are waging while they confidently try to call a bluff on virtually every expert on the planet. Let me, for a moment, be as thoughtless and selfish as they are, and answer the question being asked. Is their unvaccinated child putting my child at risk, if the vaccines I believe in work so damn well?

No. Probably not. But they are putting somebody’s vaccinated child at risk.

Let’s do some real simple math here. The variables for infection rates and vaccine effectiveness vary by disease, and the equations get pretty complicated as they interact with each other, so I’m going to round off and keep it as simple as possible. Statistically, if you expose 100 unvaccinated people to measles, 95 of them will catch it. If you expose 100 people who have had one dose of the vaccine (MMR or MMRV), 5 of those partially vaccinated people will still catch measles. If you expose 100 people who have had two doses of the vaccine, 1 of those fully vaccinated people will still catch measles. Those are the numbers, roughly. Different diseases are different. Measles is on the extreme end of both factors: It is extremely contagious, but the vaccine also works extremely well.

Let’s say a child goes on a trip to some exotic place where measles is common due to low vaccination, like India or Southern California. If that child comes in contact with measles, an unvaccinated child will almost certainly (95% chance) catch the disease, where a vaccinated child will almost certainly not (1% chance) catch the disease. The vaccinated child comes back from his vacation with a statue of Vishnu or some Mickey Mouse ears, while the unvaccinated child comes back as Patient Zero.

Let’s assume the kid has become contagious before returning from his trip. He gets on a Boeing 737 with 200 other people. Even if every single person on that flight is vaccinated, 2 of them will contract measles. Anyone who is unvaccinated will almost certainly (95% chance) catch it. You go through the airport, get your luggage, and possibly infect a few more on the way.

Monday comes around, and it’s time to go back to school. Let’s go with the national average, and say 90% of the students are vaccinated, and that child comes in contact with 500 students. Of the 50 students that are unvaccinated, 42 of them will catch measles. Out of the 450 students that are fully vaccinated, 4 of them will still catch measles.

You can adjust these numbers how you see fit: for how infectious the disease is, how effective the vaccine is, or how many people the child will come in contact with, but you will never come to an equation that justifies this kind of reckless endangerment.

I think we can stop there, and not get into shopping malls, taking a subway, visiting our newborn cousin in the hospital, etc. And we still have that list of people who cannot be vaccinated that I generously ignored for this exercise, but sure as hell would not ignore when one of them died in the real world. Statistically speaking, my kids are a hundred times more likely to be one of the 446 vaccinated children at that school who were protected than the unlucky 4 the vaccine did not work for. So yeah, I guess you got me there. I’m not worried your unvaccinated child is going to infect mine. But that doesn’t mean I can’t be pissed on behalf of the 46 students your bluff call did infect. I can be concerned about the people on the plane you infected who went off and started their own school outbreaks. And I can do everything possible to hold you accountable for the damage you’ve caused for absolutely no good reason. When you try to call a bluff like that and are wrong, you are expected to pay up.

Someone suggested that I discuss another article that analyzed a measles outbreak in Corpus Christi, TX, which compared those who were vaccinated with the MMR vaccine to those weren’t. The results are clear and relatively straightforward:

1732 children were seropositive (meaning they had antibodies to measles) and over 99% of them were vaccinated. None, and not close to none, but absolutely 0 of these children contracted measles.

74 children were seronegative (they lacked measles antibodies). Fourteen (14) of these children contracted measles.

So, let’s look at the math. All of the kids who had measles antibodies (presumably as a result of the MMR vaccine, since 99% were vaccinated) avoided the disease and its consequences. On the other hand, 18.9% of the children who lacked antibodies got sick.

Again, if this isn’t clear…0% contracted the disease if they had antibodies from vaccines, 18.9% contracted the disease if they didn’t have antibodies.

Now, the 74 children who were seronegative also were vaccinated (though the paper did not tell us how many vaccines were given, it takes at least 2 to confer full immunity). If there are no other issues (and again, the article didn’t report that) like some type of compromised immune systems in some of the 74 children), the vaccine was 96% effective in seroconverting and preventing measles.

This story is rather basic. The MMR vaccine is extremely effective in boosting the immune system to produce anti-measles anti-bodies. A small group seems to have not seroconverted for unknown reasons. But even though most of the population in this study were protected against measles, the disease is so pervasive, so pathogenic, even a small group of susceptible individuals can catch it. But because the vast majority, 96% were protected against the disease, this measles outbreak didn’t spread further.

But think about this. If the number isn’t 96%, but 70% because parents refuse to vaccinate. What happens is that the random chance that an infected child encounters an unvaccinated child increases dramatically, increasing the risk of a much larger outbreak. With all of the consequences of measles.

As I said before, it really is simple math. So simple that a vaccine denier could do it.

According to the most recent data, 12 of the cases are children and 14 are adults, and nine of 12 children were unvaccinated (2 were because parents got an exemption, and the other 7 because they were too young to be vaccinated with the MMR vaccine). In addition, it was difficult to determine the vaccination status of the adults, but we’ll focus on the children.

If you read the most obnoxious antivaccination websites (and I did it for you), you’d see claims that only 2 of the 26 were unvaccinated (simply not true or an ignorant misreading of the actual data), implying that 90% of those who caught measles were vaccinated. In fact, it’s at least 9 who were unvaccinated.

So let’s go with some simple math, just based on this small sample. But if the antivaccination lunatics are going to invent numbers, it is my job to obtain real numbers that show factually what is happening.

The outbreak is centered in Upper Manhattan and The Bronx areas of Manhattan, a total population of just under 2 million individuals. Now the outbreak is actually more focused than those areas, but it makes the math easier for the anti-science crowd.

Total population: 1,945,000

Total school age population (pdf, Appendix Table 4 and 10), which we will assume covers the the ages of the children in the measles outbreak: 550,222

I’m going to vastly oversimplify the risk of the measles outbreak, because I am aware that the antivaccine crowd is math challenged. If I used real epidemiological data, measure the risk in the exact geographical areas of the outbreak, data that I don’t have, the incidence rate would be much higher. If I did this by actual age, say 0-18 months, the risk would absolutely frighten you. But we’ll keep it simple.

Total risk for measles for vaccinated children, 3/496,850 or 6 out of one million

Total risk for measles for unvaccinated children, 9/53,372 or 169 out of one million

So, despite what you’ve heard from the antivaccination squad, the risk for contracting measles in an outbreak is nearly 30X higher in the unvaccinated group. Again, my numbers here vastly underestimate the risk, because the actual calculation would be done using data from the small area that this outbreak occurred, with the risk for the unvaccinated group probably being 10,000X higher than stated here. And I’m not even getting to risk reducing strategies like increasing the vaccination uptake rate to 95 or 96%, and the herd effect would have stopped this outbreak in its tracks.

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